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Maths Exercices

Probability of dependent events

The probability of two dependent events A and B is the probability of A times the probability of B after A occurs.


A card is chosen at random from a standard deck of 52 playing cards. Without replacing it, a second card is chosen. What is the probability that the first card chosen is a queen and the second card chosen is a jack?

The probability that the first card is a queen is 4 out of 52. However, if the first card is not replaced, then the second card is chosen from only 51 cards. Accordingly, the probability that the second card is a jack given that the first card is a queen is 4 out of 51.

The outcome of choosing the first card has affected the outcome of choosing the second card, making these events dependent.

P(queen on first pick)  =   4 
52
 
P(jack on 2nd pick given queen on 1st pick)  =   4 
51
 
P(queen and jack)  =   4   ·   4   =    16    =    4  
52 51 2652 663